One problem is that Amazon is now inviting consumers to open a direct relationship with Google or Apple. If a user makes a purchase of an Apple TV or Chromecast directly, Google or Apple now know exactly who they are.
Generally speaking, making it hard or cutting off sales channels for specific products can work to divert sales. Big retailers do it. However, if it is a product the consumer really, really wants they are going to jump through the loopholes to get it. I imagine Apple TV will eventually fall under that category.
Alternatives? Let Apple TV and Chromecast continue to be sold but place large warning messages and suggest buying a Roku or Amazon whatever device instead.